I have this same issue while using an external monitor with my MacBook Air running Big Sur. I tried the workaround that you mentioned, however, it did not solve the issue for me.
After turning the device on again (while not connected to the external monitor - workaround step 5), the wallpaper is set to the image that I selected. Once the external monitor is attached (workaround step 6), the MacBook desktop returns to the default wallpaper. When I disconnect the external monitor, the wallpaper returns to the previously selected wallpaper.
One point of detail that may prove helpful in finding a solution: my external monitor is set to be the primary display when attached. I am not sure if that is the cause, but thought it might be helpful information.
If anyone has found a solution, please let us know. I would love to stop changing my desktop wallpaper each day!
Cheers!